Problem: An electric motor operating at 1180 RPM transfers 5.0 kW of power to a gear drive through a solid circular shaft. The shaft has a length of 1 m and is supported by two bearings, one on each side of the gear drive. The shaft is shouldered, with a diameter d along most of the length but a larger diameter D at the gear. The fillet radius r and the two diameters are related by the ratios r/d = 0.15 and D/d = 1.33. The shaft is made of steel, with shear modulus G = 79 GPa and tensile yield strength Sy = 414 MPa.
The maximum shear stress ($$\tau_{max}$$) is limited to $$\frac{1}{4}$$ of the shear yield strength ($$S_{ys}$$) for steel, and the angle of twist ($$\phi$$) between the motor and gear should not exceed $$2.0^\circ$$.
Determine the diameters d and D to satisfy all conditions. Give answers to the nearest integer value (in mm).
GEAR DRIVE
BEARING BLOCK
L=1m
Stress Concentration Factor K
Ratio, r/d
Fig. 9.10 Stress concentration factor for a shouldered shaft subject to torsion.
D/d = 1.09
D/d = 1.20
D/d = 1.33
D/d = 2.0